Mathematics & AI

Mathematics & AI

Mathematics & AI is an open-access, peer-reviewed journal at the intersection of mathematics and artificial intelligence. The journal publishes original research in mathematical foundations of AI, machine learning theory, optimization, statistical learning, neural network analysis, computational mat...
Article #1021
Issue MathAI 2025 Selected Papers Special Issue
Received 04 May 2026
Accepted 15 May 2026
Published 22 May 2026

Random forest regression and Shapley additive explanation for effective dose rate estimation in high-energy neutron fields based on Bonner spectrometer measurements

A
A. Belyi
M
M. Starikovskaya
MathAI 2025 Selected Papers Special Issue
Published: May 22, 2026 Accepted: May 15, 2026 Received: May 4, 2026

Abstract

The article proposes a method for assessing the neutron energy spectrum and effective dose rate of personnel based on the readings of a Bonner spectrometer (BSS) for high-energy neutron fields. Neutron flux density can be obtained fromBSS measurements by solving the system of Fredholm integral equations of the first kind. In our paper the spectra were unfolded using supervised machine learningalgorithm ”random forest” with optimization of the model hyperparameters. The model was trained and tested on a database of 251 spectra for various powerfacilities (80% of data was used for training the model, while 20% was used fortesting it). The input features of the model were the spectrometer readings for BSSmoderator spheres and the categorical feature ”spectrum type” describing the facilityand conditions under which the spectrum was obtained. The output parametersof the model were the spectrum description in the form of a histogram for 60energy values, as well as the dose rate calculated from the spectrum for the correspondingconversion factor. Since the dataset of real spectra is small, database of104 synthetic data generated using the Frascati Unfolding Interactive Tool methodwas developed. Second model for this synthetic dataset was trainted and comparedwith the first one. The effect of the error in the initial data on the spectrumand the dose rate obtained from it was estimated by the Monte Carlo method usingrandom samples. The test dataset showed that the unfolded spectra are closein nature to the original ones and have a high correlation with them. The paperproposes a method for selecting the optimal number of moderator spheres basedon the explainable artificial intelligence method ”Shapley additive explanation”(SHAP). The SHAP method was used to demonstrate the degree of influence ofmeasurements with moderator spheres of different diameters on the spectrum prediction. It was shown that resulting spectrum is most influenced by measurementswith moderator spheres of 10” and 12”. Optimization of the choice of spheresleads to a decrease in the personnel doses during measurements. The model wastrained and calculations were performed on the JINR Multifunctional Informationand Computing Complex.

Cite this article

Chizhov, K; Belyi, A.; Starikovskaya, M. Random forest regression and Shapley additive explanation for effective dose rate estimation in high-energy neutron fields based on Bonner spectrometer measurements. Mathematics & AI 2026, 1, 18. https://enigma.ist/j/mathematics-ai/1/1/18

Full Text (PDF)